This leads us to the mathematical definition of a graph:
A graph G = (V, E) is a pair of:
- V, a set of nodes or vertices: the islands in our previous example
- E, a set of edges connecting nodes: the bridges
The Königsberg graph illustrated on the right of the preceding image can then be defined as follows:
V = [A, B, C, D]
E = [
(A, C),
(A, C),
(C, B),
(C, B),
(A, D),
(C, D),
(B, D)
]
Graphs, like many mathematical objects, are well defined. While it can be difficult to find a good visualization for some of those objects, graphs, on the other hand, suffer from the almost infinite number of ways to draw them.
